What is the integral of 1/3 sqrt(x) ?

The integral of 1/3 sqrt(x) is 2/9 x^{3/2}+C

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integral of 1/3 sqrt(x)

\int \frac{1}{3} x d x

\frac{2}{9} x^{\frac{3}{2}} + C

Solution steps

\int \frac{1}{3} x d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int x d x

Apply the Power Rule

= \frac{1}{3} \cdot \frac{2}{3} x^{\frac{3}{2}}

Simplify

\frac{1}{3} \cdot \frac{2}{3} x^{\frac{3}{2}} : \frac{2}{9} x^{\frac{3}{2}}

= \frac{2}{9} x^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{9} x^{\frac{3}{2}} + C

What is the integral of 1/3 sqrt(x) ?
The integral of 1/3 sqrt(x) is 2/9 x^{3/2}+C